119 research outputs found
Long-Time Relaxation on Spin Lattice as Manifestation of Chaotic Dynamics
The long-time behavior of the infinite temperature spin correlation functions
describing the free induction decay in nuclear magnetic resonance and
intermediate structure factors in inelastic neutron scattering is considered.
These correlation functions are defined for one-, two- and three-dimensional
infinite lattices of interacting spins both classical and quantum. It is shown
that, even though the characteristic timescale of the long-time decay of the
correlation functions considered is non-Markovian, the generic functional form
of this decay is either simple exponential or exponential multiplied by cosine.
This work contains (i) summary of the existing experimental and numerical
evidence of the above asymptotic behavior; (ii) theoretical explanation of this
behavior; and (iii) semi-empirical analysis of various factors discriminating
between the monotonic and the oscillatory long-time decays. The theory is based
on a fairly strong conjecture that, as a result of chaos generated by the spin
dynamics, a Brownian-like Markovian description can be applied to the long-time
properties of ensemble average quantities on a non-Markovian timescale. The
formalism resulting from that conjecture can be described as ``correlated
diffusion in finite volumes.''Comment: text as published, Section 4 added and other minor change
Universal Long-Time Relaxation on the Lattices of Classical Spins: Markovian Behavior on non-Markovian Timescales
The long-time behavior of certain fast-decaying infinite temperature
correlation functions on one-, two- and three-dimensional lattices of classical
spins with various kinds of nearest-neighbor interactions is studied
numerically, and evidence is presented that the functional form of this
behavior is either simple exponential or exponential multiplied by cosine. Due
to the fast characteristic timescale of the long-time decay, such a
universality cannot be explained on the basis of conventional Markovian
assumptions. It is suggested that this behavior is related to the chaotic
properties of the spin dynamics.Comment: text as in published version, minor changes in comparison with the
original on
Temperature dependence of the superconducting gap in high-Tc cuprates
It is proposed that (i) the temperature dependence of the superconducting gap
Delta(T) in high-Tc cuprates can be predicted just from the knowledge of
Delta(0) and the critical temperature Tc; and, in particular, (ii) Delta(0)/Tc
> 4 implies that Delta(Tc) is not equal to zero, while Delta(0)/Tc < 4
corresponds to Delta(Tc) = 0. A number of tunneling experiments appear to
support the above proposition, and, furthermore, show reasonable quantitative
agreement with a model (cond-mat/0308428), which is based on the
two-dimensional stripe hypothesis.Comment: Text close to the published version. Minor textual corrections in
comparison to the previous versio
On the long-time behavior of spin echo and its relation to free induction decay
It is predicted that (i) spin echoes have two kinds of generic long-time
decays: either simple exponential, or a superposition of a monotonic and an
oscillatory exponential decays; and (ii) the long-time behavior of spin echo
and the long-time behavior of the corresponding homogeneous free induction
decay are characterized by the same time constants. This prediction extends to
various echo problems both within and beyond nuclear magnetic resonance.
Experimental confirmation of this prediction would also support the notion of
the eigenvalues of time evolution operators in large quantum systems.Comment: 4 pages, 4 figure
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